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Topic: Lucy And Lily - A Game (Read 1208 times) |
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william wu
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Lucy And Lily - A Game
« on: Oct 15th, 2003, 1:22am » |
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Hey kids, check this out! It's Neat0!
http://www.math.umd.edu/~res/games.html
You can play a interesting little game called Lucy and Lily, a Java applet written by a Richard Schwartz. Basically you try to flip a pentagon on its sides such that it returns to a certain position. Anyone can understand how to play it; just read the instructions provided in the center of the screen. Click on the "NEXT" button to move to the next set of instructions.
Amazingly, the underlying mathematics working behind the scenes of this game is related to many fascinating things, including Penrose tiles, quasicrystals, the golden mean, number theory, and more. Schwartz also provides a paper that analyzes the game.
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| « Last Edit: Oct 15th, 2003, 9:09am by william wu » |
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Icarus
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Boldly going where even angels fear to tread.
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Re: Lucy And Lily - A Game
« Reply #1 on: Nov 6th, 2003, 7:15pm » |
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Finally got around to looking at this. Interesting. His proof of finiteness was more intensive than necessary, I think. All he needed was that the combined centers of the various positions for the two pentagons forms a lattice in [bbr]4. This is fairly obvious (at least that it OUGHT to form a lattice) from a geometric point of view). Once he has the lattice, only a finite number of points can lie in a fixed radius.
It is intriguing the way that with a single pentagon it is hard to figure out what way to go, but with two related like this, the most obvious thing to do turns out to be exactly the right thing.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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